Game Theory Notes- Zero Sum Games
Book called Theory of Games and Economic Behavior
o Authors: von Neumann and Morganstern
o Zero-Sum Games
Each of the outcomes in a zero sum game are constant or are zero
More commonly, zero sum games are expressed with o
Two Player Non-Zero Sum Games
When are they dominance solvable?
o Each player has a dominant strategy
o One player has a dominant strategy
o No dominant strategies; but either player has one or more dominated
strategies
IDSDS- Iterative Deletion of Stric
Solving Nash Equilibrium
Use quasi dominated strategies to solve
o Best reply method
Look for the outcome where both payoffs are selected for both players
A Nash Equilibrium is a strategy pair such that it is the best reply to the other
persons strategy
How to Solve Zero Sum Games
MINIMAX Solution- Find the Saddlepoints
o MINIMAX: In a zero sum game, the column player reckons that, for each
of his columns, row player will choose the row with the largest number in
each column. Therefore, COL should choose
Game Theory Modeling
Three uses:
Descriptive
Prescriptive
Predictive
Questions for the modeler
Zero sums or non-zero sum?
How many players?
How many strategies for each player?
Payoffs?
Preferences?
Simultaneous or sequential moves?
Perfect or i
Dominated Strategies
Neither player has a dominant strategy but either player has one or more
dominated strategies
o IDSDS
o IDSDS may lead to a single outcome which constitutes the pure strategy
equilibrium solution to the game
o IDSDS may point to the
Dominance
Golden Rule:
o If you have a dominant strategy, play it
o If you have a dominated strategy, forget it
Solve the game as if it was a standard non-zero sum game depicted in normal
(strategic) form
If a zero sum game has two numbers, solve it the s